Final answer:
Montresor kills Fortunato by chaining him to a wall in the catacombs and then enclosing him alive behind a newly built brick wall, leading to Fortunato's death by starvation and dehydration.
Step-by-step explanation:
In Edgar Allan Poe's The Cask of Amontillado, Montresor kills Fortunato by luring him into the catacombs under the pretense of verifying the authenticity of what Montresor claims to be a rare wine, the Amontillado. Once they are in the recesses of Montresor's family vaults, Montresor takes advantage of Fortunato's inebriated state and chains him to the wall. He then proceeds to build a wall of bricks to encase Fortunato alive in a niche in the catacombs, effectively sealing his fate to die of starvation and dehydration. Montresor's act of revenge is calculated and cold-blooded, as he had planned it meticulously to ensure his own impunity and Fortunato's demise.